Answer to Question #70319 in Microeconomics for William

Question

"The pricing of pharmaceutical products can be controversial. A recent example is EpiPen
produced by Mylan which is used to treat anaphylaxis. The retail price of an EpiPen is
$300, while industry sources estimate that it costs around $30 to produce each unit (i.e.
one dose). Despite this high price, Mylan sells 1 million units a year."

Based on the above information, I have been told to solve the following question:

"Assume Mylan's indirect demand function is linear: P = a – bQ, where Q is measured
in millions of units. Using the definition of the point elasticity of demand, the elasticity
you calculated in part 1 and the unit sales of EpiPen, find the values of “a” and “b” in the
above equation."

I have already found the Elasticity in Part 1, it was found to be -0.9, but I am unsure on how to proceed.

Answer 1

As P = a - b*Q, P = $300, Q = 1,000,000 units and Ed = -0.9, then using the definition of the point elasticity of demand b = |Ed| = 0.9, so:
300 = a - 0.9*1,000,000,
a = 900,300.